We present a set of optimal and asymptotically optimal sequential and parallel algorith ms for the problem of searching on an m n sorted matrix m n Our two sequential algo rithms have a time complexity ofO m log n m which is shown to be optimal Our parallel algorithm runs in O log logm log logm log n m z time usingm log logm log logm processors on a COMMON CRCW PRAM where z is a monotonically d...

Let $n_q(k,d)$ denote the smallest value of $n$ for which there exists a linear $[n,k,d]$-code over the Galois field $GF(q)$. An $[n,k,d]$-code whose length is equal to $n_q(k,d)$ is called {em optimal}. In this paper we present some matrix generators for the family of optimal $[n,3,d]$ codes over $GF(7)$ and $GF(11)$. Most of our given codes in $GF(7)$ are non-isomorphic with the codes pre...

In this thesis I present a new algorithm OPT for matrix inversion that builds on a matrix multiplication subroutine. It is combined of Strassen’s matrix inversion algorithm and Newton approximation. OPT overcomes the linear lower bound in parallel runtime of Strassen’s inversion algorithm and traditional Gaussian elimination without the log-factor more work of Newton approximation. In particula...

We give near-optimal distributions for the sparsification of large m n matrices, where m ! n, for example representing n observations over m attributes. Our algorithms can be applied when the non-zero entries are only available as a stream, i.e., in arbitrary order, and result in matrices which are not only sparse, but whose values are also highly compressible. In particular, algebraic operatio...

We prove that for any real-valued matrix X ∈ R, and positive integers r > k, there is a subset of r columns of X such that projecting X onto their span gives a

Ever since the dawn of the computer age, researchers have been trying to find an optimal way of multiplying matrices, a fundamental operation that is a bottleneck for many important algorithms. Faster matrix multiplication would give more efficient algorithms for many standard linear algebra problems, such as inverting matrices, solving systems of linear equations, and finding determinants. Eve...

A Las Vegas type probabilistic algorithm is presented for nding the Frobenius canonical form of an n n matrix T over any eld K. The algorithm requires O~(MM(n)) = MM(n) (logn) O(1) operations in K, where O(MM(n)) operations in K are suucient to multiply two n n matrices over K. This nearly matches the lower bound of (MM(n)) operations in K for this problem, and improves on the O(n 4) operations...

Phasor Measurement Units (PMUs) are in growing attention in recent power systems because of their paramount abilities in state estimation. PMUs are placed in existing power systems where there are already installed conventional measurements, which can be helpful if they are considered in PMU optimal placement. In this paper, a method is proposed for optimal placement of PMUs incorporating conve...

This article proposes an optimal method for approximate answer of stochastic Ito-Voltrra integral equations, via rationalized Haar functions and their stochastic operational matrix of integration. Stochastic Ito-voltreea integral equation is reduced to a system of linear equations. This scheme is applied for some examples. The results show the efficiency and accuracy of the method.

The purpose of this paper is to develop a methodology for solving a new type of matrix games in which payoffs are expressed with triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, the concept of solutions for matrix games with payoffs of TIFNs is introduced. A pair of auxiliary intuitionistic fuzzy programming models for players are established to determine optimal strategies...